Integer Review: Fundamentals of Integers , Rules for Multiplication , Rules for divisibility, Division Terminology, Even & Odd Integer, Rules about even & odd integer, Prime Number, Prime Factorization , Distinct Prime Number, LCM & HCF, Composite Numbers , Consecutive Integers
Class Questions : Exercise 1 Exercise 2 Exercise 3 Exercise 4 Exercise 5
Practice Questions : Solutions
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1. Divisibility by 2
A number is divisible by 2 when the digit at one’s place is even like 2, 4, 6, 8….. e.g.
a). 2345976 – can be divided by 2 as digit at one’s place is 6, which is even
b). 56345 – cannot be divided by 2 as digit at one’s place 5, which is Odd.
2.Divisibility by 3
A number is divisible by 3 if addition of all the digits of the number is 3, or in multiple of 3 or divided by 3. e.g.
a). 59 – addition is 5 + 9 = 14 is not a multiple of 3, so cannot be divided be 3.
b). 92364 – addition is 9+2+3+6+4 =24, 24 is multiple of 3 and can be divided by 3.
3.Divisibility by 4
A number is divisible by 4 if last two digits can be are divided by 4. e.g.
a). 2368 – is divisible by 4 as 68 can be divided by 4.
b). 4582 – is not divisible by 4 as 82 cannot be divided by 4.
4.Divisibility by 5
A number is divisible by 5 if the last digit of number is either 0 or 5. e.g.
a). 236895, 25840, 25, 26830 all can be divided by 5.
5.Divisibility by 6
A number is divisible by 6 if the number is divided by 2 and 3 both. e . g.
a). 636 – can be divided by 2 as well as 3.
b). 424 – cannot be divisible by 6 because it can be divided by 2 but not by 3.
So the important is that number has to be divided by 2 and 3 both.
6.Divisibility by 8
A number is divided by 8 when last three digits of the number can be divided by 8. e.g.
a). 56,648 – can be divided by 8 as last three digits 648 is divided by 8.
7.Divisibility by 9
A number is divisible by 9 when addition of digits of number comes as 9 or in multiple of 9. e.g.
a). 963459 = 9+6+3+4+5+9 = 36, which is a multiple of 9.
8.Divisibility by 10
A number is divisible by 10 if the last digit of the number is 0. e.g.
a). 25,860 the last digit is 0 so it can be divided by 0.
9.Divisibility by 11
A number is divided by 11 if the difference of the sum of digits in odd places and the sum of digits in even places starting from ones place is either 0 or divisible by 11. e.g.
a). 5846 –
Sum of digits in odd place =6+8 =14
Sum of digits in even place = 5+4 =9
Difference = 14- 9 = 5
So this number cannot be divided by 11.
b). 2673 –
6+3 =9
2+7=9
9-9=0
This number can be divided by 11.
10.Divisibility by 12
A number is divisible by 12 if the addition of digits comes as 3 or in multiple of 3 and last two digits has to be divisible by 4. So rules for divisibility by 3 and 4 both have to be applied. e.g
a) 3720 – addition of digits is 12, which is a multiple of 3
and last two digits 20 are divided by 4.
So this number is divisible by 12.
